How can I get a cabinet projection camera?
Demonstrating in 2D what is going on:



Mathematically it should be correct to render with a orthographic camera
and later transform the image. I think this is the easiest method when
you have multiple objects (so you do not have to add modifiers to each).
First you should shear in 2D (skewing) the rendered image then (if needed)
stretch to get the correct aspect.

Original:



Sheared:



Streched:



Most raster graphics editors have the tools to preform the above
transformations. This can also be done in the compositor using a
Blend texture and the Displace node.